How do the principal axes of inertia depend on the symmetry of an object? Describe the...

How do the principal axes of inertia depend on the symmetry of an object? Describe the principal axes of inertia for a bowling pin that has rotational symmetry about one axis.

Expert Solution

When an object is rotating about a fixed axis due to the symmetry of the object about that axis sometimes we can’t differentiate between snapshots of the object at different rotation angles i.e. the mass distribution of object doesn’t change. Generally, these axes pass through center of mass(COM) and are called principle axes. For example, consider a cylinder which has the axis passing through the COM and parallel to axis of cylinder as the principle axis. The moment of inertia tensor is a diagonal matrix for these principle axes.

For a bowling pin axis passing through COM and parallel to the length of pin is the principle axis of inertia and has rotational symmetry.

genius_generous answered 2 years ago

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